For controlling the operation of a walking assisting device for assisting a human being to walk or the movement of a bipedal walking robot, it is necessary to sequentially grasp a floor reaction force acting on a leg of the human being or the bipedal walking robot (specifically, a force acting on the landing area of the leg from the floor). Grasping the floor reaction force makes it possible to grasp a moment or the like that acts on joints of the leg of the bipedal movable body, and also to determine a desired assistive force for the walking assisting device or a desired drive torque for each joint of the bipedal walking robot based on the grasped moment or the like.
One known process of grasping the floor reaction force is disclosed in Japanese laid-open patent publication No. 2000-249570, for example. According to the disclosed process, since the waveform of time-depending changes in the floor reaction force on each leg periodically changes at the time the bipedal movable body walks steadily, the floor reaction force on each leg is grasped as a combined value (linear combination) of trigonometric functions having respective different periods which are 1/n (n=1, 2, . . . ) of the walking period. The weighting coefficient of each of the trigonometric functions at the time the trigonometric functions are combined is of a predetermined value for each bipedal movable body or a value produced by adjusting the predetermined value depending on the terrain.
According to the above process, since the floor reaction force on each leg is grasped for one step or a plurality of steps of the bipedal movable body, it is difficult to grasp the floor reaction force accurately if the gait of the bipedal movable body changes sequentially. For increasing the accuracy of the grasped floor reaction force, the weighting coefficients of the trigonometric functions have to be established for each bipedal movable body or have to be adjusted depending on the terrain or the like. Therefore, it is difficult to grasp the floor reaction force accurately by reducing the effect of the environment in which the bipedal movable body moves and the difference between individual units of the bipedal movable body.
Some known bipedal walking robots have force sensors such as six-axis force sensors or the like mounted on the ankle and foot of each leg, and grasp a floor reaction force based on output signals from those force sensors. According to a known process, a bipedal walking robot is caused to walk on a force plate laid on the floor, and a floor reaction force is grasped from an output signal from the force plate.
If floor reaction forces on the legs of a human being are to be recognized based on output signals from force sensors, then since the force sensors need to be mounted on the ankles and feet of the human being, the force sensors tend to present an obstacle to the walking of the human being in the normal living environment. Use of the force plate is only effective to grasp the floor reaction plate only in the environment in which the force plate is used.
In order to eliminate the above drawbacks, the applicant of the present application has proposed a method of estimating a floor reaction force as disclosed in Japanese patent application No. 2002-39201 or PCT/JP02/06467. The principles of the proposed method will be described below with reference to FIGS. 1(a) and 1(b). Motion states of a bipedal movable body (motion states of legs during walking) include a one-leg supporting state in which, as shown in FIG. 1(a), only one (the forward leg in the direction of travel in the figure) of the legs 2, 2 of a bipedal movable body 1 is landed, and a two-leg supporting state in which, as shown in FIG. 1(b), both the legs 2, 2 are landed.
If a total floor reaction force which acts on the legs 2, 2 from a floor A is represented by F, then the total floor reaction force F is equal to a floor reaction force acting on the landed leg 2 in the one-leg supporting state shown in FIG. 1(a), and is equal to a combination of floor reaction forces Ff, Fr acting respectively on the legs 2, 2 in the two-leg supporting state shown in FIG. 1(b). In an absolute coordinate system Cf that is fixed with respect to the floor A on which the bipedal movable body 1 moves, it is assumed that an acceleration a of the center G0 of gravity of the bipedal movable body 1 has components ax, az respectively in an X-axis direction (horizontal direction of travel of the bipedal movable body 2) and a Z-axis direction (vertical direction), and the total floor reaction force F acting on the bipedal movable body 1 has components Fx, Fz respectively in the X-axis direction and the Z-axis direction. The dynamic equation of the center G0 of gravity (specifically, the dynamic equation with respect to the translation of the center G0 of gravity) is expressed as the following equation (1):T(Fx, Fz−M·g)=M·T(ax, az)  (1)(where M: the weight of the bipedal movable body, g: the gravitational acceleration)
The parentheses T( , ) on both sides of the equation (1) represent a two-element vector. In the present specification, the notation T( , ) expresses a vector.
The dynamic equation of the center G0 of gravity thus serves as a relational expression indicating that the product of the acceleration a of the center G0 of gravity and the weight M of the bipedal movable body 1 is equal to a combination of the gravitational force (=M·g) acting on the center G0 of gravity and the total floor reaction force F.
Therefore, if the acceleration a=T(ax, az) of the center G0 of gravity of the bipedal movable body 1 is grasped, then an estimated value of the total floor reaction force F=T(Fx, Fz) can be obtained according to the following equation (2), using the acceleration a, the value of the weight M of the bipedal movable body 1, and the value of the gravitational acceleration g:T(Fx, Fz)=M·T(ax, az+g)  (2)
In the one-leg supporting state shown in FIG. 1(a), since the floor reaction force acting on the single leg 2 that is being landed is equal to the total floor reaction force F, an estimated value of the total floor reaction force F acting on the single leg 2 can be obtained according to the equation (2).
The weight M which is required to obtain the estimated value of the floor reaction force F can be grasped in advance by measurements or the like. The position of the center G0 of gravity and the acceleration a can sequentially be grasped by a known process using the outputs of sensors such as sensors for detecting the bent angles (rotational angles) of the joints of the bipedal movable body 1, acceleration sensors, and gyrosensors, as described in detail later on.
In the two-leg supporting state shown in FIG. 1(b), the floor reaction force Ff on the front leg 2 has components Ffx, Ffz in the respective X- and Z-axis directions, the floor reaction force Fr on the rear leg 2 has components Frx, Frz in the respective X- and Z-axis directions. Th total floor reaction force F has components Fx, Fz expressed by Ffx+Frx, Ffz+Frz, respectively, in the respective X- and Z-axis directions, and the dynamic equation of the center G0 of gravity is expressed as the following equation (3):T(Ffx+Frx, Ffz+Frz−M·g)=M·T(ax, az)  (3)
In the two-leg supporting state, it is assumed that, as shown in FIG. 1(b), the floor reaction forces Ff, Fr on the respective legs 2, 2 act from particular regions 12f, 12r of the legs 2, 2 (e.g., ancles) near the lower ends thereof toward the center G0 of gravity of the bipedal movable body 1. In this case, between the positions of the particular regions 12f, 12r of the legs 2, 2 and the floor reaction forces Ff, Fr acting on the respective legs 2, 2, there is satisfied a certain relational expression, i.e., a relational expression indicating that the orientations of line segments interconnecting the center G0 of gravity and the particular regions 12f, 12r of the legs 2, 2 (the orientations of positional vectors of the particular regions 12f, 12r with respect to the center G0 of gravity) are equal to the orientations of the floor reaction forces Ff, Fr acting on the respective legs 2, 2.
Specifically, referring to FIG. 1(b), if the position of the center G0 of gravity has coordinates (Xg, Zg), the position of the particular region 12f of the front leg 2 has coordinates (Xf, Zf), and the position of the particular region 12r of the rear leg 2 has coordinates (Xr, Zr) in the absolute coordinate system Cf, then the above relational expression is given as the following equation (4):(Zf−Zg)/(Xf−Xg)=Ffz/Ffx(Zr−Zg)/(Xr−Xg)=Frz/Frx  (4)
From the equation (4) and the equation (3), the following equations (5), (5′) are obtained:Ffx=M·{ΔXf·(ΔZr·ax−ΔXr·az−ΔXr·g)}/(ΔXf·ΔZr−ΔXr·ΔZf)Frx=M·{ΔXr·(−ΔZf·ax+ΔXf·az+ΔXf·g)}/(ΔXf·ΔZr−ΔXr·ΔZf)  (5)Ffz=M·{ΔZf·(ΔZr·ax−ΔXr·az−ΔXr·g)}/(ΔXf·ΔZr−ΔXr·ΔZf)Frz=M·{ΔZr·(−ΔZf·ax+ΔXf·az+ΔXf·g)}/(ΔXf·ΔZr−ΔXr·ΔZf)  (5′)(where ΔZf=Xf−Xg, ΔZf=Zf−Zg, ΔXr=Xr−Xg, ΔZr=Zr−Zg)
Therefore, if the acceleration a=T(ax, az) of the center G0 of gravity of the bipedal movable body 1 is grasped and the positions (which are expressed by ΔXf, ΔZf, ΔXr, ΔZr in the equations (5), (5′)) of the particular regions 12f, 12r of the legs 2, 2 with respect to the center G0 of gravity of the bipedal movable body 1 are grasped, then it is possible to obtain estimated values of the floor reaction forces Ff=T(Ffx, Ffz), Fr=T(Frx, Frz) on the respective legs 2 according to the equations (5), (5′), using the acceleration a, the positions of the particular regions 12f, 12r, the value of the weight M of the bipedal movable body 1, and the value of the gravitational acceleration g.
In this case, the weight M which is required to obtain the estimated values of the floor reaction forces Ff, Fr can be grasped in advance by measurements or the like. The acceleration a of the center G0 of gravity, the position of the center G0 of gravity, and the positions of the particular regions 12f, 12r with respect to the center G0 of gravity can sequentially be grasped by a known process using the outputs of sensors such as sensors for detecting the bent angles (rotational angles) of the joints of the bipedal movable body 1, acceleration sensors, and gyrosensors, as described in detail later on.
It has been found that the estimated values of the vertical components Ffz, Frz of the floor reaction forces on the legs in the two-leg supporting state, which are determined by the method of the prior application are not necessarily of satisfactory accuracy. This is because the floor reaction forces Ff, Fr on the respective legs do not necessarily act from the particular regions 12f, 12r of the legs 2, 2 toward the center G0 of gravity of the bipedal movable body 1. The estimated values of the vertical components of the floor reaction forces which become large under the influence of the weight of the bipedal movable body 1 tend to suffer a larger error than their components in the direction of travel.
In view of the above shortcomings, it is a task of the present invention to provide a floor reaction force estimating method which is capable of grasping the vertical component of a floor reaction force acting on each leg in a two-leg supporting state, accurately in real-time according to a relatively simple process, the floor reaction force estimating method being particularly suitable for grasping a floor reaction force on a human being as a bipedal mobile body.